Question

In a sample of 117 residences, 65 had reduced their water consumption. If we were to construct a 95% confidence interval for the proportion of residents who reduced their water consumption. What is our standard error? Round to 3 decimal places.

Answer 1

Solution :

Given that,

n = 117

x = 65

Point estimate = sample proportion = = x / n = 65/117=0.556

1 -   = 1- 0.556 =0.444

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

standard error SE=((( * (1 - )) / n) =(((0.556*0.444) /117 )=0.046

Margin of error = E = Z/2   * ((( * (1 - )) / n)

= 1.96 (((0.556*0.444) /117 )

E = 0.0900

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.556-0.0900 < p < 0.556+0.0900

0.466< p < 0.646

The 95% confidence interval for the population proportion p is : 0.466,0.646